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Unconditional Uniqueness for the Cubic Gross‐Pitaevskii Hierarchy via Quantum de Finetti

- Thomas Chen, C. Hainzl, N. Pavlovic, R. Seiringer
- Mathematics
- 11 July 2013

We present a new, simpler proof of the unconditional uniqueness of solutions to the cubic Gross‐Pitaevskii hierarchy in ℝ3 . One of the main tools in our analysis is the quantum de Finetti theorem.… Expand

Existence of a Stable Polarized Vacuum in the Bogoliubov-Dirac-Fock Approximation

- C. Hainzl, Mathieu Lewin, É. Séré
- Physics
- 4 March 2004

According to Dirac’s ideas, the vacuum consists of infinitely many virtual electrons which completely fill up the negative part of the spectrum of the free Dirac operator D0. In the presence of an… Expand

The BCS Functional for General Pair Interactions

- C. Hainzl, E. Hamza, R. Seiringer, J. P. Solovej
- Mathematics
- 29 March 2007

The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous… Expand

Critical Temperature and Energy Gap for the BCS Equation

- C. Hainzl, R. Seiringer
- Physics
- 27 January 2008

We derive upper and lower bounds on the critical temperature Tc and the energy gap � (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two- body… Expand

The critical temperature for the BCS equation at weak coupling

- R. Frank, C. Hainzl, S. Naboko, R. Seiringer
- Mathematics
- 26 April 2007

For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ»0. We derive necessary and sufficient conditions… Expand

The mean‐field approximation in quantum electrodynamics: The no‐photon case

- C. Hainzl, Mathieu Lewin, J. P. Solovej
- Physics
- 31 March 2005

We study the mean‐field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering or… Expand

Microscopic Derivation of Ginzburg-Landau Theory

- R. Frank, C. Hainzl, R. Seiringer, J. P. Solovej
- Physics
- 19 February 2011

We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises… Expand

Spectral properties of the BCS gap equation of superfluidity

- C. Hainzl, R. Seiringer
- Mathematics
- 4 February 2008

We present a review of recent work on the mathematical aspects of the BCS gap equation, covering our results of [arXiv:0801.4159] as well our recent joint work with Hamza and Solovej… Expand

Mass Renormalization and Energy Level Shift in Non-Relativistic QED

- C. Hainzl, R. Seiringer
- Physics
- 1 May 2002

Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized… Expand

Existence of Atoms and Molecules in the Mean-Field Approximation of No-Photon Quantum Electrodynamics

- C. Hainzl, Mathieu Lewin, É. Séré
- Physics
- 31 May 2006

The Bogoliubov–Dirac–Fock (BDF) model is the mean-field approximation of no-photon quantum electrodynamics. The present paper is devoted to the study of the minimization of the BDF energy functional… Expand

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